Hydrodynamic Simulation Of Cold, Dense Objects Evaporating In A Hot, Tenuous Plasma.

The evaporation of cold dense objects in relatively hot tenuous plasmas is a subject of interest to several groups of scientists, including astrophysicists, researchers in magnetic fusion energy (MFE), and researchers in inertial confinement fusion (ICF). Analytic models based upon the steady-state hydrodynamic conservation equations are routinely used to estimate the characteristics of the evaporating material. We have developed a computer code that solves the time-dependent hydrodynamic conservation equations. In our simulations, we apply the code to examine the validity of the steady-state models, and to examine the effect of flux-limited thermal conduction in pellet injected tokamak plasmas. We find that the steady-state model examined (Cowie, McKee, Astrophys. J., 211: 135-146, 1977) is reproduced by the time dependent calculations only when assumptions made by the model are included in the simulations. The most significant assumption is found to be the neglect of the cooling wave launched into the hot plasma as energy is conducted to the cloud. Neglecting the cooling wave results in overestimating the mass ablation rate and underestimating the cloud lifetime. Thus, the applicability of the model in astrophysical and MFE environments is compromised. The cooling wave has less of an effect in ICF experiments since the plasma is steadily reheated by the laser pulse. We have simulated the evaporation of fuel pellets injected into tokamak plasmas and compared our results to data from experiments. By matching the calculated and measured excitation radiation emitted by the ablating pellet, we are able to estimate the flux-limit parameter (f) in the flux-limited conduction expression (q = fnv$\sb{\rm t}$kT). We obtain good agreement with the data by using a flux-limit parameter f = 0.2. This is one order of magnitude larger than those typically required in ICF simulations, and is near a maximum value (f $\simeq$ 0.32) estimated by distribution function and zero current arguments. Our calculations reproduce the data without the need to invoke any shielding mechanism to protect the pellet from the plasma. It is common in MFE calculations to require that a neutral gas surround the pellet as it penetrates the plasma so as to reduce the energy flux to the pellet. We find that this neutral gas shield is not present. Finally, the steady-state model of Cowie and McKee does not reproduce our pellet injection results. A steady-state does appear to develop but the density decays spatially as 1/r$\sp{3}$, and the expanding ablatant is sonic (M = 1), scalings which are quite different from those of Cowie and McKee.Ph.D.Plasma physicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128050/2/8720256.pd